Consider a spherical shell of radius at temperature

PHYSICS · Subjective · ISC · Mathematics · Physics · Calculus

Problem

Consider a spherical shell of radius

R

at temperature

T

. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume

u=\frac{U}{V}\propto T^4

and pressure

p=\frac{1}{3}\left(\frac{U}{V}\right)

. If the shell now undergoes an adiabatic expansion, the relation between

T

and

R

is: